Guardian Forces are important to work with - in many battles they're the difference between life and death. Here are the GFs in the game and where to find them.

Quezacotl: In classroom at beginning
Shiva: In classroom at beginning
Ifrit: in Fire Cavern - first task
Siren: drawn from Elvoret during Dollet mission
Diablos: from magic lamp you get from Cid after Dollet mission
Brothers: end of Tomb of Unknown King area
Carbuncle: defeating Iguion after the sewers
Leviathan: when you finish NORG off
Pandemona: from Fujin at Balamb City
Tonberry: from Tonberry King near the ruins with Odin
Cerberus: beat Cerberus in Galbadia Garden

Be sure to have your GFs learn BOOST. When you have a GF in battle, hold down your select button. A prompt will appear in the lower-right saying "75". Just rapidly tap to raise this up, making sure you pause whenever you see an X. You can get all the way up to 250. I set my control to auto-repeat so I don't wear out my tapping finger. Note that Cactaur, Carbuncle, Diablos and Cerebus can't do this.